Electronic Scientific Journal
 
Diagnostics, Resource and Mechanics 
         of materials and structures
Рус/Eng  

 

advanced search

IssuesAbout the JournalAuthorContactsNewsRegistration

2019 Issue 1

All Issues
 
2024 Issue 5
 
2024 Issue 4
 
2024 Issue 3
 
2024 Issue 2
 
2024 Issue 1
 
2023 Issue 6
 
2023 Issue 5
 
2023 Issue 4
 
2023 Issue 3
 
2023 Issue 2
 
2023 Issue 1
 
2022 Issue 6
 
2022 Issue 5
 
2022 Issue 4
 
2022 Issue 3
 
2022 Issue 2
 
2022 Issue 1
 
2021 Issue 6
 
2021 Issue 5
 
2021 Issue 4
 
2021 Issue 3
 
2021 Issue 2
 
2021 Issue 1
 
2020 Issue 6
 
2020 Issue 5
 
2020 Issue 4
 
2020 Issue 3
 
2020 Issue 2
 
2020 Issue 1
 
2019 Issue 6
 
2019 Issue 5
 
2019 Issue 4
 
2019 Issue 3
 
2019 Issue 2
 
2019 Issue 1
 
2018 Issue 6
 
2018 Issue 5
 
2018 Issue 4
 
2018 Issue 3
 
2018 Issue 2
 
2018 Issue 1
 
2017 Issue 6
 
2017 Issue 5
 
2017 Issue 4
 
2017 Issue 3
 
2017 Issue 2
 
2017 Issue 1
 
2016 Issue 6
 
2016 Issue 5
 
2016 Issue 4
 
2016 Issue 3
 
2016 Issue 2
 
2016 Issue 1
 
2015 Issue 6
 
2015 Issue 5
 
2015 Issue 4
 
2015 Issue 3
 
2015 Issue 2
 
2015 Issue 1

 

 

 

 

 

V. D. Solovei

VARIATIONAL PRINCIPLE FOR THE VELOCITIES OF PARTICLES OF A VISCOPLASTIC STRIP UNDER ROLLING

DOI: 10.17804/2410-9908.2019.1.064-069

Plane flow of a viscoplastic strip under rolling is considered. Tangential friction stresses at the flow–roll interface and at contact of the flow region with the rigid strip ends are specified approximately by the Prandtl friction law. A variational principle is proved for particle velocities with account of the convection flow.

Keywords: viscoplastic strip rolling, stationary flow of a strip, convective flow, variational principle, local potential

References:

1. Ilyushin A.A. The Deformation of a Visco-Plastic Solid. Uchenye Zapiski Mosk. Gos. Univ., Ser. 2, 1940, vol. 39, pp. 3–81. (In Russian).

2. Моsolov P.P., Miasnikov V.P. Variational methods in the theory of the fluidity of a viscous-plastic medium. Journal of Applied Mathematics and Mechanics, 1965, vol. 29, no. 3, pp. 545–577. DOI: 10.1016/0021-8928(65)90063-8.

3. Freydental A., Geyringer Kh. Matematicheskie teorii neuprugoy sploshnoy sredy [Freudenthal Alfred M., Geiringer Hilda. The Mathematical Theories of the Inelastic Continuum. In: Handbuch der Physik, Bd.VI, Berlin, Göttingen, Heidelberg, Springer-Verlag, 1958, pp. 229–433]. Moscow, Fizmatgiz Publ., 1962, 432 p. (In Russian).

4. Kolmogorov V.L. Mekhanika obrabotki metallov davleniem [Mechanics of Metal Forming]. Moscow, Metallurgiya Publ., 1986, 688 p. (In Russian).

5. Alekseev A.E. Nonlinear laws of dry friction in contact problems of linear theory of elasticity. Journal of Applied Mechanics and Technical Physics, 2002, vol. 43, iss. 4, pp. 622–629. DOI: 10.1023/A:1016018118184.


PDF      

Article reference

Solovei V. D. Variational Principle for the Velocities of Particles of a Viscoplastic Strip under Rolling // Diagnostics, Resource and Mechanics of materials and structures. - 2019. - Iss. 1. - P. 64-69. -
DOI: 10.17804/2410-9908.2019.1.064-069. -
URL: http://eng.dream-journal.org/issues/2019-1/2019-1_250.html
(accessed: 11/21/2024).

 

impact factor
RSCI 0.42

 

MRDMS 2024
Google Scholar


NLR

 

Founder:  Institute of Engineering Science, Russian Academy of Sciences (Ural Branch)
Chief Editor:  S.V. Smirnov
When citing, it is obligatory that you refer to the Journal. Reproduction in electronic or other periodicals without permission of the Editorial Board is prohibited. The materials published in the Journal may be used only for non-profit purposes.
Contacts  
 
Home E-mail 0+
 

ISSN 2410-9908 Registration SMI Эл № ФС77-57355 dated March 24, 2014 © IMACH of RAS (UB) 2014-2024, www.imach.uran.ru